$$ \int \frac{ds}{a+bs^2} $$

Question

hartnn · Answer

know the general formula for 
1/(x^2+a^2)
?

anonymous · Answer

trig substitution?

hartnn · Answer

if, u can't use direct formula.....u can substitute...

anonymous · Answer

What do you mean by general formula?

hartnn · Answer

$\ \huge 16. \int \frac{1}{x^2+a^2}dx=a^{-1}\tan^{-1}(\frac{x}{a})+c
\$

hartnn · Answer

first u need to divide by b to be able to use it...

anonymous · Answer

I've understood that much. What to substitute? 

A better question: what general logic (other than having seen this problem before, which won't be of help in the future) do I use when deciding what to substitute?

It seems with the x^2 the cos^2+sin^2=1 identity may be useful.

hartnn · Answer

when there is + ans a square term.. u think of 1+tan^2x = sec^2 x 
so that u can substitute here s= tan

hartnn · Answer

*and

anonymous · Answer

OK- I've got that integral- is there any general rule for deciding how to substitute, or is it mainly intuition?

hartnn · Answer

seen my tutorial, right ? i've given table of substitution there. .

hartnn · Answer

but yeah, that comes with practice....

anonymous · Answer

Tables are artificial, only useful for engineers. But thanks.

hartnn · Answer

true... intuition comes with practice....